For questions on dice, a small throwable object with multiple resting positions, used for generating random numbers. This makes dice suitable as gambling devices for games like craps, or for use in non-gambling tabletop games.

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How many dice would I need to get an $n$ of a kind 100% of the time?

For example, if I wanted to get two of a kind, I would need seven dice. This is because even if the first six were 1, 2, 3, 4, 5, 6, the next one would have to make a pair out of the previous dice. ...
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4answers
182 views

Find the probability that the final score is 4 in a dice game with two throws

A game uses an unbiased die with faces numbered 1 to 6. The die is thrown once. If it shows 4 or 5 or 6 then this number is the final score. If it shows 1 or 2 or 3 then die is thrown again and the ...
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2answers
38 views

Having two random generated natural numbers between 1 and 255, and generate out of it natural number between 1 and 256

Let's say you have two cube with 255 sides and you have to use them to simulate a single cube with 256 sides, how can I do it? $f(n)$ and $g(n)$ returns random number between 1 and 255. I thought ...
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2answers
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Rolling two dice… [closed]

Let $A_n$ be the number of fives, $B_n$ the number of sixes and $C_n$ the number of eights in $n$ rolls of two dices. For which n do we have: $E(A_n) < E(min(B_n,C_n))$ ?
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1answer
45 views

exactly $k$ distinct values in $n$ $n$-sided dices

We roll $n$ $n$-sided dices. What is the probability of getting exactly $k$ different values? From the union bound (as every possible $k$ sequence might contain the $k$ different results), I think the ...
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1answer
48 views

Rolling a certain total with a dice

Suppose you roll a $k$-sided die repeatedly, totaling your scores as you go, until you reach or surpass $n$. (For a real-world usage ... if you have a non-looping game board and only move forward, ...
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1answer
47 views

Suppose we roll 10 fair six-sided dice. Probability of getting exactly two 2's and three 3's?

Here's my solution, but as usual with combinatorics problems, I tend to be convinced of my errors too early. So I'd like to know what you guys think. Is this correct? $\frac{\binom{10}{2} ...
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0answers
24 views

How good of an approximation is a normal probability distribution for sum of dice rolls?

I want to know how well the normal distribution explains the sum of rolls with n dice with s sides. The mean value and the variance of the dice rolls are $$\mu=n\frac{s+1}{2}$$ and ...
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1answer
25 views

Approximation of distributions with dice

I want to know what dice to roll to get a given probability distribution(mainly normal distributions but exponential distribution would also be helpful). I want a function $f$ so that ...
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2answers
64 views

Probability of dice with a cumulative successes

Needing some Math help! I'm working out part of a system for a game I'm working on, and I need to know if I need to tweak some things, so I'm checking to see if it all adds up (no pun intended). ...
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3answers
42 views

What is the probability that dice are rigged?

Scenario We are given a single six-sided die. We produce a sequence of $n$ dice rolls, all of them rolling six. We do not know whether the die is fair or not. How can we calculate the probability ...
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7answers
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Is it possible to create a completely random integer between 1 and 13 using standard dice in a D&D dice kit?

I am asking if it is possible to choose a random integer using a certain set of dice. Assume for these calculations that the dice are perfectly randomly distributed. There are 7 dice in a set, with ...
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2answers
36 views

A probability question - Dice Throw

Sum of three dice (six faced) throws is $15$. What is the probability that first throw was $4$? The way I thought of solving this was... - Given - sum of second and third throw is $11$ - Probability ...
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3answers
111 views

Probability of getting a sum of 14 when rolling 11 dice

So, this is a probability and combinatorics problem... I'm not sure how to solve this. I assume that in P(A) = m/n, n is 6^11, but I don't know how to calculate the number of ways to get a sum of 14 ...
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3answers
50 views

What is the probability of two dice getting a sum of 7 without a two?

I am currently working on conditional probability and I am somewhat confused about how exactly to complete this problem. I know that to find conditional probability that you utilize: $$P(A|B) = ...
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1answer
32 views

Simple dice probability question [closed]

Just a simple quick question. Five dice are thrown at the same time, all results are independent of each other. The dice are regular dice, with 6 sides. What is the probability that exactly three ...
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1answer
66 views

A fair die is rolled nine times. What is the probability that 1 appears three times, 2 and 3 each appear twice, 4 and 5 once and 6 not at all?

A fair die is rolled nine times. What is the probability that 1 appears three times, 2 and 3 each appear twice, 4 and 5 once and 6 not at all? My approach is fairly simple. The dice is fair, so we ...
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1answer
32 views

Optimal strategy in the following game:

In this game, 12 hidden D6s are rolled and summed. The player is given the total of the rolled dice. The player will then guess a number from 1 to 6. If there is a unrevealed dice with that number, ...
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0answers
44 views

Expected number of rolls on a 200 sided die to roll a 1? [duplicate]

We have a 200 sided fair die with faces numbered 1 through 200 and want to know how many rolls are expected to roll a 1. How would I go about calculating this?
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1answer
52 views

What's more likely with 7 dice - Straight, Full House, or 3-of-a-Kind

Here's a problem I'm having. I have 7 dice. I want to rank the difficulty of achieving a particular 5 dice combination after all 7 dice have been rolled. A straight is when at least 5 of the seven ...
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1answer
45 views

Dice Probabilities - How often does 3, 4, 5 show up in 5 dice on one roll?

I want to find out the probability for rolling 5 dice and the result containing at least 3, 4, and 5 without caring what the other 2 numbers are. I'm not very familiar with this kind of probability so ...
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1answer
37 views

Is this Event Mutally Exclusive?

I am trying to calculate the following, however I'm unsure on whether this event would be Mutally Exclusive or Independent. Can someone help with finding the probability of the Intersection? P(A) ...
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3answers
47 views

How to handle dice probability? ie, how much more likely would 3 six sided dice give a higher sum than 3 four sided dice?

I am playing at making my own table-top gaming system/rules and I wanted to have a better handle on how likely different dice combinations will give a higher result than one another. I know that a six ...
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5answers
149 views

Dice roll probability, at least 9 total?

If I have two dice with $6$ sides each, what is the probability of me rolling atleast $9$ total? I think I'm correct when thinking that the probability of rolling a $9$ is $\frac{4}{36}$, that is ...
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1answer
44 views

Normal distribution with dice

I'm wondering how to control the normal distribution that comes from summing dice rolls only using different numbers of dice, different combination of types of dice (d4, d6, d8, d10, d12, d20) and ...
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0answers
44 views

Probability of succesful rolls of different sided dies

This seems so simple, but I'm not sure how to calculate it. I have one six-sided die and one 12-sided die. What is the probability that, on a roll of both dice, that the six-sided die will win? ...
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1answer
38 views

The name for predicting future rolls of dice based on the past

My friends and I were playing a game where you roll dice and you bet money on what picture it's going to land on and I began reasoning with myself that if I tallied up what pictures the dice landed on ...
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2answers
44 views

Expected number of rolls?

Suppose a fair six-sided die has the following sides: 1, 1, 1, 1, 4, 4. The die is rolled twice. The mixed outcomes [1,4] and [4,1] are considered "successes" while the outcomes [1,1] and [4,4] are ...
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2answers
47 views

Probability with a 7-sided dice

I have this : "We roll a 7-sided dice n times. What is the lower value of n to have 60% of chance to have 2 same value" And I don't know how I can resolve this ... I know that the result is 5 but ...
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1answer
36 views

expected number of gold you can collect.

expected number of gold you can collect. you have a six sided dice and n points 1 to n. there some golds in any points. initially you are in position 1. if you reach any point you can collect all the ...
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2answers
41 views

What are the chances of drawing this unique combination of 3 coloured dice from 6 dice?

I'm having trouble understanding why one (or both) of my methods is wrong. Here is the problem. Let's say I have 6 dice: 2 yellow, 2 green, 2 red. I'm going to draw 3 dice from the 6 dice, and I ...
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2answers
154 views

Why is the sum of the rolls of two dices a Binomial Distribution? What is defined as a success in this experiment?

I know that a Binomial Distribution, with parameters n and p, is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which ...
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1answer
48 views

Propability of M-faced dice rolling a greater result than an N-faced dice ( M<N) and expected value of the absolute difference?

Hello I have a game-mechanic which goes like this: Two-sides are rolling numbers. The defender rolls between [1,Armor_Value] , attacker rolls between [1,Damage_Value]. If the attacker_roll> ...
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2answers
59 views

4 Sided dice - flawed logic?

If we had a 4 sided dice (numbers 1,2,3,4 on the faces) and rolled it 6 times and recorded the results. What would be the probability that we rolled the same number 3 or more times? (Such as rolling ...
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2answers
37 views

Chance of rolling one skull with these three dice?

Let's say I have three 6-sided dice. One is red, one is green, one is yellow. The red dice have 3 skulls on 3 of its faces, the other faces are blank. The green dice have 1 skull each. The yellow ...
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2answers
30 views

What are the chances of drawing 2 shotguns in Zombie Dice in this situation?

I'm rusty on probability and, even so, I don't think I know how to deal with this situation. Here's the problem. Let's say I have a cup of $n$ dice. Each dice face has either a shotgun, a brain, or ...
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1answer
42 views

Dice rolls probability

Given a six-faced die with six distinctly marked faces, what is the probability that a toss will turn-up any one of the six faces. If three of the six faces are red and three blue, what is the ...
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1answer
52 views

Estimating the number of sides of a die

A friend of mine inspired this question: Given a fair die, can one accurately estimate (within some margin) the size of the die given enough rolls? For example: If I roll a die 1000 times and all the ...
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2answers
56 views

Why are the probability of rolling the same number twice and the probability of rolling pairs different?

Two scenarios: 1. Using one die, roll a 6 twice. $\frac16\times\frac16=\frac1{36}$ Rolling two dice roll the same number (a pair). $\frac6{36}=\frac16$ Why are these two probabilities ...
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2answers
50 views

Probability with 8 number of dice

Eight identical dice are rolled simultaneously. In how many possible outcomes each of the six numbers appears at least once? I got result as $\left(\dfrac 16\right)^8.$ And I think I missed some ...
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2answers
114 views

4 sided dice rolls - a probability question

If we had a 4 sided dice (numbers 1,2,3,4 on the faces) and rolled it 5 times and recorded the results. What would be the probability that we rolled the same number exactly 3 times? What about 3 or ...
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1answer
186 views

Sum of resulting values of dice

We have thrown with $n$ dice. The sum of resulting values is $k$. We are looking for a function $f$ which gives the number of throws, with we can construct $k$ with $n$ dice. Some example for ...
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1answer
25 views

Expected amount of different diced numbers

I roll n regular, d-sided dices. What is the expected amount of different numbers on the dices? Or equivalently: What is the expected amount of numbers that have not been diced at all? Example: ...
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1answer
44 views

Dice Game - Probability Theory

There are many dice problems on here so there could be duplicate. If there is I apologize. Here is the question. The game is given as follows: you are given 5 dice, and the goal of the game is to get ...
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1answer
26 views

Finding an $f(x,y,n)$ such that $round[f(x,y,n)] = \lfloor\frac xn \rfloor + \lfloor\frac yn \rfloor$

Problem: I have an equation: $$\left\lfloor\frac xn\right\rfloor + \left\lfloor\frac yn\right\rfloor$$ I need to find an equation that does NOT use the floor function, but will take those same two ...
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1answer
36 views

Probability of hitting a certain sum with dices

Using $5$ $6$-faced dices, what's the probability of hitting a cumulative sum $S$, on a particular roll (each roll incorporates all $5$ dices ), if $15 \leq S\leq 20$? I reckon this particular ...
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2answers
68 views

Regarding combinatorics on dice…

The problem: If you are to roll a die five times, what is the probability the fifth die is not a repetition? Apparently the answer is $$\frac{6\cdot5^4}{6^5}$$ but I don't really see why. What ...
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0answers
82 views

Probability of rolling n dice to match another set of dice, d, given r rolls (like yahtzee)

(Note: I will eventually code this, but i'm primarily interested in the math behind it) I'm trying to create a function in Java to calculate the probability of getting a desired outcome from n rolled ...
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0answers
28 views

Multiple Dice Roll Probability (With Forumla)

I'm having the trouble of determining probability over multiple die rolls. I'm working with this formula. $$\frac{d20+d(\textrm{skill}) - \textrm{difficulty}}{d20+d(\textrm{skill})}$$ Basically, you ...
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2answers
83 views

Conditional probability rolling two dice

Two fair dice are rolled. What is the conditional probability that at least one lands on 6 given that the dice land on different numbers? I already know the answer, but am having some trouble ...